if a woman encounters violence, she immediately runs to the closest man.
Jim I'm sorry to burst your bubble, but this simply isn't true. Personally I have been harassed and had people be violent to me, and I've never had a man help me at all. I can say "Me Too" many times, and the closest thing I've had is men just stare.
To be honest, after being harassed and a victim of violence I took up studying martial arts. I studied self-defense and mixed martial arts for about seven year. I know I can't beat up everyman in the world, but I do know how to defend myself and how to deal with harassment. I went to a school full of women, so please know, we don't just expect mean to protect us from violence.